Damage to the central nervous system as a result of hypoxic-ischemic injury at birth is a major cause of life-long mental and neurodevelopmental handicap. Unfortunately, no therapeutics have yet been identified which, when administered to neonates following birth asphyxia, significantly lessen the extent of brain damage or improve outcome. Recent studies in the investigators' laboratories, and in many others, indicate that erythropoietin (Epo) is a "natural" neuroprotectant. During hypoxemia Epo is produced rapidly and abundantly by the microglia, and in a paracrine fashion this Epo binds to specific Epo receptors on neurons. This binding has at least three salutary actions; 1) it induces antiapoptotic factors that preserve neurons which would otherwise undergo apoptosis, 2) it reduces perineuronal inflammation, and 3) it has direct antioxidant effects. An improved understanding of the biology of Epo during human neuronal development has led to experiments where recombinant Epo (rEpo) was administered in an attempt to reduce post-hypoxic-ischemic brain damage. Indeed, when rodents were subjected to a variety of experimental brain injuries, rEpo administration, even up to six hour after the event, reduced subsequent brain injury by 50-70%. However, the doses of rEpo required were considerably higher (5,000 U/kg/dose) than those traditionally used by neonatologists to stimulate erythropoiesis and reduce erythrocyte transfusions (100 to 200 U/kg/dose). Before a clinical trial can be designed to test the efficacy of very-high-dose rEpo administration in reducing post-asphyxic brain injury, basic Phase I/II information on pharmacokinetics, biologic effect, and safety must be obtained. Therefore, the investigators designed a multi-centered, open-labeled, dose-escillation trial of very-high-dose rEpo administration to neonates who have had birth asphyxia. The study will be performed using the consortium known as the Florida Collaborative Neonatology Trials Group and the follow-up will be accomplished using the State of Florida Early Intervention Program (EIP), in which all study patients will be enrolled. Within three hours of birth, each eligible patient will receive one dose of rEpo intravenously (n=5 will receive 1,000 U/kg; the subsequent n=5 will receive 2,500 U/kg; the final n=5 will receive 5,000 U/kg). The doses will be increased to the next highest group if such is sanctioned after review by the Data Safety Monitoring Board. Any patient who has a lumbar puncture performed during the first week of life will have natural Epo and rEpo in their spinal fluid determined to assess the degree of penetration of rEpo across the blood brain barrier. They will also have free iron and total isoprostanes in the spinal fluid quantified as measures of oxidative stress and oxidative damage. The effect of rEpo on plasma free iron and plasma total Isoprostanes following hypoxia will be assessed at intervals following rEpo treatment. Pharmacokinetics of rEpo in this population will be determined and safety parameters evaluated. To aid the design of a subsequent Phase III trial, neurodevelopmental outcome will be measured in the EIP program clinics at six and 12 months or life.